Find all vectors in that have the same length as and are orthogonal to when is each of the following:

- ;
- ;
- ;
- .

- If , let be a vector such that and . Then we have
Since the lengths are the same and we also have

Therefore, or .

- If , let be a vector such that and . Then we have
Since the lengths are the same and we also have

Therefore, or .

- If , let be a vector such that and . Then we have
Since the lengths are the same and we also have

Therefore, or .

- If , let be a vector such that and . Then we have
Since the lengths are the same and we also have

Therefore, or .